That basket of goods is supposed to be representative of a person's needs (although there is debate about that). If the person's aggregate purchasing power across the basket went down, then the value of their salary went down. They're receiving less value for doing the same work.

Most things are interconnected. Yes, gas might not directly affect a specific company, but it will eventually due to things like inputs, shipping, etc going up. And yes, even the people on the supplier side getting raises will affect it.

"People like to think of X% inflation meaning that every dollar is worth less"

At an aggregate level that is how it works. The basket of goods costs more. The person's purchasing power has been reduced. The the number of dollars needed to purchase the same basket of goods is higher. So yes, the dollar is worth less. As you point out, not every product costs more, but most do eventually as the effects ripple (some go down, but usually though changes in technology/production/etc).

I understand that the company needs to stay competitive and they would need to increase revenue to increase salary. Usually that isn't a large enough increase to affect competitive prices for the actual workers (executives and management are different). Of course that assumes being competitive with other onshore companies. If competing with offshore companies in LCOL areas, then it's going to be nearly impossible to compete (see things like steel production in the US).